The proof is the same as [1]} and for the convenience of the reader we sketch out the proof.
From the regularity of the solution we see that the equation can be defined in the classical manner and
\(f^{\prime }(T_{\ast })=u(y,T_{\ast })\partial _{x}u(y,T_{\ast })-u(x,T_{\ast })\partial _{x}u(x,T_{\ast })+\Lambda u(y,T_{\ast })-\Lambda u(x,T_{\ast }).\) 
